2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152062A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.5 pages, AMS-TeX, no FiguresDifferential Geometry$Pin$-structures on surfaces and quadratic formstext